Finite Group Databasebeta

← C2×#22612005 #33240362

Subgroups — C2×#22612005 #33240362

Order 18688.

790 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989022C211yesmaximal, characteristic, complemented
2C2×#17988962C211yesmaximal, characteristic, complemented
3C2×#17988704C211yesmaximal, characteristic, complemented
4#22612005C218yesmaximal, direct product factor
5C2×#17988407C211yesmaximal, characteristic, complemented
6C2×#17988401C211yesmaximal, characteristic, complemented
7C2×#17988400C211yesmaximal, characteristic, complemented
8C2×#509×C73C211yesmaximal, characteristic, complemented
9C22×D584C2211yescharacteristic
10C22×#11924013—21no—
11C2×#14556598—21no—
12C2×#14556587—21no—
13#17989022—22no—
14#17989022C2214yescomplemented
15C2×#14556534—21no—
16C2×#14556532—21no—
17C2×#14556531C2211yescharacteristic
18#17988962—22no—
19#17988962C2214yescomplemented
20#17988704—22no—
21#17988704C2214yescomplemented
22C2×#14556527C2211yescharacteristic
23C2×#14556518—21no—
24C2×C8×Dic73C2211yescharacteristic
25#17988407C2214yescomplemented
26#17988401C2214yescomplemented
27#17988400C2214yescomplemented
28C2×#135×C73C2211yescharacteristic
29C22×D8×C73C2211yescharacteristic
30#509×C73—22no—
31#509×C73C2214yescomplemented
32C2×SD32×C73—21no—
33C2×D16×C73—21no—
34C2×M32×C73C2211yescharacteristic
35C22×D292—21no—
36C22×C22⋊D73—42no—
37C2×D584—21no—
38C2×D584—21no—
39C2×D584—21no—
40C2×D584—21no—
41C2×D584—21no—
42C2×D584C2312yes—
43C2×#11924013—24no—
44C2×#11924013—41no—
45C2×#11924013—41no—
46C2×#11924013—42no—
47#14556598—24no—
48#14556598—42no—
49C2×#11924012—21no—
50C2×#11924012—41no—
51C22×#10596831—41no—
52C22×#10596831D411yescharacteristic
53#14556587—24no—
54#14556587—42no—
55C2×C4×Dic73D411yescharacteristic
56#14556534—24no—
57#14556532—24no—
58#14556531—21no—
59#14556531C2312yes—
60C2×#11924003—21no—
61#14556527—21no—
62#14556527C2312yes—
63#14556518—24no—
64C8×Dic73D412yes—
65C8×Dic73C2312yes—
66C2×#41×C73—21no—
67C22×D4×C73—21no—
68#135×C73—21no—
69#135×C73—21no—
70#135×C73D412yescomplemented
71#135×C73C2312yes—
72C2×Q16×C73D411yescharacteristic, complemented
73C2×SD16×C73—21no—
74C2×D8×C73—21no—
75C2×D8×C73—21no—
76C2×D8×C73—21no—
77C2×D8×C73—21no—
78C2×D8×C73—21no—
79C2×D8×C73D411yescharacteristic, complemented
80C2×D8×C73C2312yes—
81C22×C8×C73C2311yescharacteristic
82SD32×C73—24no—
83D16×C73—24no—
84M32×C73—21no—
85M32×C73C2312yes—
86C2×C16×C73—21no—
87C23×D73—41no—
88C2×D292—22no—
89C2×D292—41no—
90C2×D292—41no—
91C2×D292—41no—
92C2×D292—41no—
93C2×D292—41no—
94C2×C22⋊D73—48no—
95C2×C22⋊D73—88no—
96C22×Dic73—21no—
97D584—22no—
98D584—22no—
99D584—41no—
100D584—41no—
101#11924013—44no—
102#11924013—44no—
103#11924012—22no—
104#11924012—41no—
105#11924012—44no—
106C2×#10596831—41no—
107C2×#10596831—44no—
108C2×#10596831D811yescharacteristic
109C2×#10596831D811yescharacteristic
110C2×#10596831D812yes—
111C2×#10596831C2×D412yes—
112C4×Dic73—21no—
113C4×Dic73C2×D412yes—
114#11924003—22no—
115C24×C73—41no—
116#41×C73—22no—
117#41×C73—22no—
118#41×C73—41no—
119#41×C73—41no—
120C2×Q8×C73—21no—
121C2×D4×C73—21no—
122C2×D4×C73—22no—
123C2×D4×C73—41no—
124C2×D4×C73—41no—
125C2×D4×C73—41no—
126C2×D4×C73—41no—
127C2×D4×C73—41no—
128C2×D4×C73—41no—
129C22×C4×C73—41no—
130C22×C4×C73C2×D411yescharacteristic
131Q16×C73—21no—
132Q16×C73C2×D412yescomplemented
133SD16×C73—22no—
134SD16×C73—22no—
135D8×C73—21no—
136D8×C73—22no—
137D8×C73—22no—
138D8×C73—41no—
139D8×C73—41no—
140D8×C73C2×D412yescomplemented
141C2×C8×C73C2×D411yescharacteristic
142C2×C8×C73C2×D411yescharacteristic
143C2×C8×C73C2×D411yescharacteristic
144C2×C8×C73#4111yescharacteristic
145C2×C8×C73#4111yescharacteristic
146C2×C8×C73C2411yescharacteristic
147C16×C73—22no—
148C23×C73—41no—
149C23×C73—42no—
150C23×C73—84no—
151C23×C73—81no—
152C23×C73—81no—
153C23×C73AGL(1,ℤ/8)11yescharacteristic
154C22×D73—42no—
155C22×D73—84no—
156C22×D73—81no—
157C22×D73—81no—
158Q8×C73—22no—
159Q8×C73—41no—
160D4×C73—22no—
161D4×C73—42no—
162D4×C73—42no—
163D4×C73—42no—
164D4×C73—42no—
165D4×C73—41no—
166D4×C73—81no—
167D4×C73—81no—
168C2×C4×C73—41no—
169C2×C4×C73—42no—
170C2×C4×C73—42no—
171C2×C4×C73#12111yescharacteristic
172C2×C4×C73#12111yescharacteristic
173C2×C4×C73C2×D811yescharacteristic
174C2×C4×C73C2×D811yescharacteristic
175C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C73C22×D411yescharacteristic
177C22⋊D73—816no—
178C2×Dic73—24no—
179C2×Dic73—22no—
180D292—42no—
181D292—42no—
182D292—81no—
183D292—81no—
184C8×C73#12111yescharacteristic
185C8×C73#12111yescharacteristic
186C8×C73C22×D411yescharacteristic
187C8×C73C2×#4111yescharacteristic
188#10596831—42no—
189#10596831C2×D812yes—
190#10596831C2×D812yes—
191C22×C73—22no—
192C22×C73—42no—
193C22×C73—84no—
194C22×C73—82no—
195C22×C73—82no—
196C22×C73—162no—
197C22×C73—162no—
198C22×C73#45911yescharacteristic
199C22×C73#45911yescharacteristic
200C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
201C2×D73—84no—
202C2×D73—82no—
203C2×D73—162no—
204C2×D73—162no—
205C4×C73—42no—
206C4×C73#45911yescharacteristic
207C4×C73#45911yescharacteristic
208C4×C73C2×#12111yescharacteristic
209C4×C73C22×D811yescharacteristic
210Dic73—24no—
211C2×#2213—731nomaximal, Sylow
212C2×C73—21no—
213C2×C73—21no—
214C2×C73—82no—
215C2×C73—162no—
216C2×C73#221312yescomplemented
217C2×C73C2×#45911yescharacteristic
218D73—162no—
219C2×#509—731no—
220C2×#509D7311yescharacteristic, complemented
221C2×#493—731no—
222C2×#443—731no—
223#2213—738no—
224C2×#364—731no—
225C2×#361—731no—
226C2×#361—731no—
227C73C2×#221311yescharacteristic, complemented, Sylow
228C2×#135C2×D7311yescharacteristic
229C22×D8—731no—
230C22×D8—1461no—
231C22×D8C2×D7311yescharacteristic
232C2×#131—1461no—
233C2×#127—1461no—
234#509—22no—
235#509—734no—
236#509—1462no—
237#509C2×D7314yescomplemented
238C2×SD32—21no—
239C2×SD32—1461no—
240C2×D16—21no—
241C2×D16—1461no—
242C2×M32—731no—
243C2×M32C2×D7311yescharacteristic
244#493—734no—
245#493—1462no—
246#443—734no—
247#443—1462no—
248C2×#108—731no—
249C2×#104—1461no—
250C2×C4×C8—731no—
251#364—734no—
252#361—734no—
253#361—734no—
254C2×#41—21no—
255C22×D4—21no—
256C22×D4—2922no—
257C22×D4—1461no—
258#135—21no—
259#135—21no—
260#135C22⋊D7312yescomplemented
261#135C22×D7312yes—
262C2×Q16C22⋊D7311yescharacteristic, complemented
263C2×SD16—21no—
264C2×D8—21no—
265C2×D8—21no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—2921no—
270C2×D8—2921no—
271C2×D8—2922no—
272C2×D8—732no—
273C2×D8—1464no—
274C2×D8—1461no—
275C2×D8—1461no—
276C2×D8—1461no—
277C2×D8—1461no—
278C2×D8—1461no—
279C2×D8C22⋊D7311yescharacteristic, complemented
280C2×D8C22×D7312yes—
281#131—2922no—
282#131—1464no—
283C2×M16—2921no—
284C2×M16—1461no—
285C22×C8—2921no—
286C22×C8—731no—
287C22×C8C22×D7311yescharacteristic
288#127—2922no—
289#127—1464no—
290C2×C42—731no—
291SD32—24no—
292SD32—1464no—
293D16—24no—
294D16—1464no—
295M32—21no—
296M32—732no—
297M32—1461no—
298M32C22×D7312yes—
299C2×C16—21no—
300C2×C16—1461no—
301#108—732no—
302#108—1461no—
303#104—1464no—
304C4×C8—732no—
305C4×C8—732no—
306C24—41no—
307C24—2921no—
308#41—22no—
309#41—22no—
310#41—41no—
311#41—41no—
312C2×Q8—21no—
313C2×D4—21no—
314C2×D4—22no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—2928no—
322C2×D4—2921no—
323C2×D4—2921no—
324C2×D4—2921no—
325C2×D4—2921no—
326C2×D4—2921no—
327C2×D4—5848no—
328C2×D4—1462no—
329C22×C4—41no—
330C22×C4—1461no—
331C22×C4D4×D7311yescharacteristic
332Q16—21no—
333Q16C2×C22⋊D7312yescomplemented
334SD16—22no—
335SD16—22no—
336D8—21no—
337D8—22no—
338D8—22no—
339D8—41no—
340D8—41no—
341D8—2924no—
342D8—2924no—
343D8—2921no—
344D8—2921no—
345D8—1462no—
346D8—1462no—
347D8C2×C22⋊D7312yescomplemented
348M16—2921no—
349M16—2924no—
350M16—1462no—
351C2×C8—2921no—
352C2×C8—2924no—
353C2×C8—731no—
354C2×C8—731no—
355C2×C8—732no—
356C2×C8—732no—
357C2×C8D4×D7311yescharacteristic
358C2×C8C2×C22⋊D7311yescharacteristic
359C2×C8C2×C22⋊D7311yescharacteristic
360C2×C8#1192402711yescharacteristic
361C2×C8#1192402711yescharacteristic
362C2×C8C23×D7311yescharacteristic
363C42—732no—
364C42—1461no—
365C16—22no—
366C16—1462no—
367C23—41no—
368C23—42no—
369C23—84no—
370C23—81no—
371C23—81no—
372C23—2922no—
373C23—5844no—
374C23—5841no—
375C23—5841no—
376C23#1455661511yescharacteristic
377Q8—22no—
378Q8—41no—
379D4—22no—
380D4—42no—
381D4—42no—
382D4—41no—
383D4—42no—
384D4—42no—
385D4—81no—
386D4—81no—
387D4—2922no—
388D4—2922no—
389D4—58416no—
390D4—5841no—
391D4—5841no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—1464no—
396C2×C4—1462no—
397C2×C4#1455656311yescharacteristic
398C2×C4#1455656311yescharacteristic
399C2×C4D8×D7311yescharacteristic
400C2×C4D8×D7311yescharacteristic
401C2×C4#1455661511yescharacteristic
402C2×C4C2×D4×D7311yescharacteristic
403C8—2922no—
404C8—732no—
405C8—732no—
406C8#1455656311yescharacteristic
407C8#1455656311yescharacteristic
408C8C22×C22⋊D7311yescharacteristic
409C8C2×#1192402711yescharacteristic
410C22—22no—
411C22—42no—
412C22—84no—
413C22—82no—
414C22—82no—
415C22—162no—
416C22—162no—
417C22—5844no—
418C22—5842no—
419C22—11682no—
420C22—11682no—
421C22#1798878011yescharacteristic
422C22#1798878011yescharacteristic
423C22C2×#1455661511yescharacteristic
424C4—42no—
425C4—1464no—
426C4#1798878011yescharacteristic
427C4#1798878011yescharacteristic
428C4C2×#1455656311yescharacteristic
429C4C2×D8×D7311yescharacteristic
430C2—21no—
431C2—21no—
432C2—82no—
433C2—162no—
434C2—11682no—
435C2#2261200512yesdirect product factor
436C2C2×#1798878011yescharacteristic
subgroupG/H
centerC22#17988780
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC2×#509×C73C2
socleC22×C73#459
hypercenterC2×#509D73
hypocenterC73C2×#2213
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989022C2semidirect
2. C2×#17988962C2semidirect
3. C2×#17988704C2semidirect
4. #22612005C2direct (N × H)
5. C2×#17988407C2semidirect
6. C2×#17988401C2semidirect
7. C2×#17988400C2semidirect
8. C2×#509×C73C2semidirect
14. #17989022C22semidirect
19. #17988962C22semidirect
21. #17988704C22semidirect
25. #17988407C22semidirect
26. #17988401C22semidirect
27. #17988400C22semidirect
31. #509×C73C22semidirect
70. #135×C73D4semidirect
72. C2×Q16×C73D4semidirect
79. C2×D8×C73D4semidirect
132. Q16×C73C2×D4semidirect
140. D8×C73C2×D4semidirect
216. C2×C73#2213semidirect
220. C2×#509D73semidirect
227. C73C2×#2213semidirect
237. #509C2×D73semidirect
260. #135C22⋊D73semidirect
262. C2×Q16C22⋊D73semidirect
279. C2×D8C22⋊D73semidirect
333. Q16C2×C22⋊D73semidirect
347. D8C2×C22⋊D73semidirect
435. C2#22612005direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179890222
C2×#179889622
C2×#179887042
#226120052
C2×#179884072
C2×#179884012
C2×#179884002
C2×#509×C732
C2×#221373